The notion of disjointness was introduced by Harry Furstenberg in 1967 in his seminal
paper [1]} for dynamical systems where the spaces are measurable space, and the applications are measure-preserving transformations, and for homeomorphisms of compact spaces, generally to study fluid flows. After that, the notions of disjoint universality, disjoint hypercyclicity, and disjoint topological transitivity were introduced and studied independently for operators by Bès and Peris in [2]}, and Bernal González in [3]}.
